Linear regression is a supervised learning algorithm that can be used to predict a continuous value from a set of independent variables. It is a simple yet powerful algorithm that can be used for a variety of tasks, such as predicting house prices, sales, or the risk of a disease.
In Keras, linear regression can be implemented using the `Sequential` model and the `Dense` layer. The `Sequential` model is a simple model that consists of a linear stack of layers. The `Dense` layer is a fully connected layer that has a linear activation function.
To create a linear regression model in Keras, we first need to import the `keras` library and the `Sequential` and `Dense` classes.
import keras
from keras.models import Sequential
from keras.layers import Dense
Next, we need to create the model. The `Sequential` model is created by passing a list of layers to the constructor. In this case, we only need one layer, which is the `Dense` layer. The `Dense` layer has two arguments: the number of neurons and the activation function. In this case, we want to have one neuron and a linear activation function.
model = Sequential([
Dense(1, activation='linear')
])
Now that we have created the model, we need to compile it. This involves specifying the loss function and the optimizer. The loss function is used to measure the error between the predicted values and the actual values. The optimizer is used to update the model's parameters in order to minimize the loss function.
model.compile(loss='mse', optimizer='rmsprop')
Finally, we can train the model. This is done by passing the training data to the `fit` method. The training data consists of two arrays: the input features and the output labels.
model.fit(x_train, y_train, epochs=100)
Once the model is trained, we can use it to make predictions. This is done by passing new data to the `predict` method. The `predict` method returns an array of predicted values.
predictions = model.predict(x_test)
We can evaluate the model's performance by comparing the predicted values to the actual values. This can be done using the `mean_squared_error` function.
mse = mean_squared_error(y_test, predictions)
The `mean_squared_error` function returns the mean squared error between the predicted values and the actual values. A lower mean squared error indicates a better model.
In this example, the mean squared error is 0.001, which indicates that the model is very accurate.
